Shadows

Sometimes when we see shadows of objects, the shadows are
very sharp and distinct, looking remarkably like the objects
themselves. Other times the shadows are "fuzzy" or lacking in a
definite edge.

What causes fuzzy shadows?

Under what conditions is a shadow formed in the first
place?

In the diagram above we see the requisite pieces. There must be
a light source, an object illuminated by the source, and there
must be some sort of screen. Various things serve as screens
including walls, floors, furniture, etc.

EXPERIMENTAL RESULTS:

If we experiment with ordinary objects of various sizes and
with light sources of various types, we find there are three
things that affect the fuzziness of a shadow:

Whether the object is close to or far from the screen.
Close to the screen, the shadow is more distinct. (Light source
to screen distance remains the same.)

Whether the light is close to or far from the object. Close
to the object, the shadow is fuzzier. Object distance to screen
distance remains the same.)

Whether the light source is large or small. Larger sources
tend to produce fuzzier shadows. (Relative positions of the
source, object and screen remains the same.)

ANALYSIS:

Adjusting the locations of source and screen affects the
degree of "fuzziness" of the shadow, and never really
causes the shadow to become totally clear. Changing the size of
the light source, however, has the ability to change whether there
is any fuzziness at all.

CONCLUSION: The size of the light source is the cause
of the fuzzy shadows!

THEORY:

If we could shrink a light source down to a single point, we
would find the light traveling outwards in all directions,
traveling in straight lines. This is the point we wish you to
begin thinking about light - namely that it originates from a
single point, whether it's one point or many.

Now if this diverging light hits an object which doesn't allow
the light to pass through it (also called opaque), part of
the light will be blocked. This forms areas that are lighted, and
an area that isn't. The unlighted area is called the shadow.

With light coming from a very small source, the shadow's edges
are clear and the shadow is well-defined. The won't be any
"fuzziness" if we have a single, small source.

With two point sources, there would be two separate shadows.
Where the two shadows overlapped, there can be no light and it
would be perfectly dark. Where one's shadow is lighted by the
other, the shadow would be an intermediate color or gray. The
outside areas lighted by both sources would be light.

The diagram shows what the shadow might look like on a screen,
assuming the object is a cylinder held perpendicular to the page
and parallel to the screen.

Adding a third source, makes the shadow area more complicated,
with areas lighted by all three sources, areas lighted by two
sources, areas lighted by only one source, and finally an area
unlighted by any source.

As we move from 1 source to 3 sources, the gradations of light
at the edges of the central, dark shadow become increasingly
complex. When we move to a real source, composed of a very large
number of sources, we find the grays blending smoothly together,
varying from light to dark gradually. This is the "fuzzy" area,
the "fuzzy shadow" that we get when the source has size.

Why are there fuzzy shadows? Because most real sources of light
have size: many, many points emitting light, creating many, many
shadows, each point helping to fill in the shadows created by
other points.

But how do we explain the observations we made during our lab
work? In a word, GEOMETRY.

Compare the amount of gray or fuzziness on the three screens at
different distances:

At A, the gray, fuzzy area has expanded a little. However, at
B, the expansion has proceeded and the area that is fuzzy is now
larger. Finally at C, the fuzzy area is at its greatest in this
diagram. As the screen gets further from the object, the degree of
fuzziness expands due to the geometry of the situation, moving
further and further out on a continually increasing triangle.

By moving the source further from the object, the angle is
reduced and therefore the amount of fuzziness is also
reduced...through Geometry!

ECLIPSES:

The shadow cast by our moon is a cone-shaped area of complete
darkness as shown below. To either side of the cone is a gray
area. The completely dark area is called the umbra, while
the gray area is called the penumbra. Wherever the moon
goes, it carries this dark umbra with it.

Now, as the moon orbits the earth, most of the time the umbra
completely misses it. Only on rare occasions does the umbra come
close to the surface, and even more rarely does it strike the
earth's surface at all. When it does, however we are treated to a
special event, a total solar eclipse. The sun will not be
seen at all if you are in the umbra as no light can get there. If
you are in the penumbra, part of the sun can be seen but not all.

The earth's shadow (due to the sun) is also a cone-shaped umbra
surrounded by a penumbra. It is larger than the moon's, though,
due to the much larger size of the earth.

In fact, the umbra from the earth is so large that the entire
moon can fit inside it. Due to the angle of the moon's orbit and
its changing distance from the earth, though, the moon doesn't
often cross the umbra in the best possible way. When it does,
however, we are treated to a total lunar eclipse.

So other than being fun (like the shadow in Peter Pan),
important in all areas of art, and an interesting phenomenon,
shadows mostly tell us about the nature of light. Light tends to
travel in straight lines and can be blocked by material objects.
It doesn't bend around them and fill in the area behind, at least
at the scale we are considering here.